Question: Divide the following complex numbers: $\dfrac{9 e^{11\pi i / 6}}{ e^{\pi i / 3}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $9 e^{11\pi i / 6}$ ) has angle $\frac{11}{6}\pi$ and radius 9. The second number ( $ e^{\pi i / 3}$ ) has angle $\frac{1}{3}\pi$ and radius 1. The radius of the result will be $\frac{9}{1}$ , which is 9. The angle of the result is $\frac{11}{6}\pi - \frac{1}{3}\pi = \frac{3}{2}\pi$ The radius of the result is $9$ and the angle of the result is $\frac{3}{2}\pi$.